Can I turn a procedural displacement into geometry?
Yes, you can.

But you need to use different modifiers for this.

First, remove subsurf and use multires+displacement:



You need to use multires for simplicity in creating normal map for game engine. With normal map you can create a detailed object without complex geometry, that important for game engines.



For creating normal map, unwrap your object (U), crate material and put image for baking in it, and in render settings select normal type and press bake.



After baking, save resulted image and setup it as normal map. Now you can remove multires, apply displace (for basic shape) and export your model in game engine.